Question

The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel straight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the actual track (the shaded region).

Answer 1

First we calculate the area of each semicircle (half the area of the full circle)
and we substract them to get the area of the curved shaded part

1/2 * [ pi * (80/2)**2 ] - 1/2 * [ pi * (60/2)**2 ] = (800-450)pi = 350*pi m2

the area of the full circle   (both sides) ------------2*350*pi m2--750*pi m2

The area of the straight line = 2 * (100 *10) = 2000 m2

Total Area = 2000 +700*pi m2 = 4198 m2